Dynamics of Miscible Interfaces and the Effects of Korteweg Stresses

可互溶界面之研究及Korteweg應力之影響

陳慶耀(Ching-Yao Chen) ； Eckart Meiburg ； 王儷霖(Li-Lin Wang)

《中國航空太空學會學刊》 33卷1期 (2001/03) Pp. 7-15

https://doi.org/10.6124/TAASRC.200103_33(1).02

摘要

數值模擬黏滯度及密度差異與無因次流量(Peclet number)對垂直毛細管中，輸對稱可互溶流體界面之作用。模擬結果顯示黏滯度差異對流體界面有顯著影響。因不同黏滯比，此界面變化可產生連續上昇之指狀流場或持續形成上昇水泡。於黏滯比不甚顯著，較小之Pe值時，水泡形成受較強之擴散作用影響而較不明顯。同時亦考慮Korteweg應力與流場因混合產生之流場散度之影響。當Korteweg常數爲正數峙，上昇指狀界面呈較尖之前沿，同時上昇速度亦較快；反之，負Korteweg常數則產生慢且鈍之指狀前沿界面，速度散度影響在此流場則非常微小。若考慮強制流量之推移，Korteweg應力與流場散度則對指狀前沿速度無顯著改變。

關鍵字

可互溶界面 ； Korteweg應力 ； 數值模擬

並列摘要

Miscible flows in vertical capillary tubes are investigated by axisymmetric numerical simulations for a variety of viscosity and density ratios, and at different dimensionless flow rates (Peclet numbers) for two different scenarios: naturally buoyant flow and injecting net flow. For naturally buoyant flow, the simulations indicate a strong effect of the viscosity ratio on the flow. Different viscosity ratios are seen to lead to either a continuously rising finger, or to a sequence of bubbles that pinch off from the main finger. The influence of the Peclet number is seen to depend on the viscosity ratio. For the moderate viscosity contrast, and at relatively low values of Pe, the tendency for the bubbles to pinch off from the main finger is somewhat impeded by the effects of diffusion. At large Pe values, the tendency towards bubble generation is more pronounced. Furthermore, the effects of Korteweg stresses and non-vanishing divergence are addressed. A positive Korteweg stress constant results to a faster and more pointed finger, and a negative constant leads to a slower and blunter finger. The effect of divergence is found to be small. For the flows with injection, both the influences of Korteweg stresses and divergence are insignificant to the finger tip velocity for large Peclet number.

並列關鍵字

Miscible interface ； Korteweg stresses ； Numerical simulations